Arithmetic *

  • In our younger days, we had to study Arithmetic.
  • Reading, (W)riting and (A)rithmetic were the Three R’s.
  • Burmese version is Ah Thone Lone (for Ah Phut, Ah Yay and Ah Twet.
  • Had to study some subjects in English and Burmese.


  • Our elders used the textbook by Workman.
  • We use the book by U Pann Yi (who adapted/translated Workman’s book).

Rapid Mental Calculation

  • During our younger days, there was an Indian lady who could do large calculations in her head.
  • There was Trachtenberg’s method of rapid mental calculation.
    To keep his sanity in a prison, Tratchenberg developed a method to perform arithmetic operations quickly.

Short cuts

  • Before the advent of calculators and computers, it was advantageous to learn some short cuts.
  • (a) To find the square of a number ending in five.
  • 115 x 115 = (11 x 12) x 100 + 25 = 13225.
  • It can be done easily in the head.
  • It follows from Algebra.
  • (10a + 5) (10a + 5) = 100a^2 + 100a + 25 = 100a(a+1) + 25
  • (b) use “Casting out the nines” to check if multiplication is correct.
  • It follows from “Modulo Arithmetic”.
  • A number, which is a power of 10, when divided by 9 gives a remainder of 1.


Some use abacus. There are several variations.

(a) Most abacus has two sets of bead :
Two beads (with a weight of 5)
Five beads (with a weight of 1)
(b) Some use less beads :
One bead (with a weight of 5)
Four beads (with a weight of 1)
(c) Currently, some after-school classes in the USA teach abacus

Computational Aids

Mechanical, electro-mechanical and electronic calculators became computational aids. The early calculators were beaten by a proficient abacus user.

Computers, PCs and smart devices are ubiquitous.

Categories: A B C

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